HEC Research Papers Series,
HEC Paris

Abstract: This paper develops a belief update rule under ambiguity, motivated by the maxim: in the face of new information, retain those conditional beliefs in which you are more confident, and relinquish only those in which you have less confidence. We provide a preference-based axiomatisation, drawing on the account of confidence in beliefs developed in Hill (2013). The proposed rule constitutes a general framework of which several existing rules for multiple priors (Full Bayesian, Maximum Likelihood) are special cases, but avoids the problems that these rules have with updating on complete ignorance. Moreover, it can handle surprising and null events, such as crises or reasoning in games, recovering traditional approaches, such as conditional probability systems, as special cases.

Keywords: Belief Update; Ambiguity; Multiple Priors; Confidence; Complete ignorance; Update on Surprising or Null Events

JEL-codes: D81; D83

42 pages, May 16, 2019

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